In an application of Krasner's lemma, to show that the algebraic closure $\theta$ of $Q_p$ is not topologically complete, one shows that the dimension of $\theta$ is at most infinitely countable over $Q_p$, and so by Blaire category theorem we finish.
For this, I need the following result:
If we consider ${Q_p}^{n+1}$ as the space of polynomial of degree at most $n$ (in the obvious way), then if we have a separable irreducible polynomial $f$, then if we slightly perturb its coefficients, it remains irreducible.
This isn't hard once I can prove my main question:
If we perturb the coefficients, then the roots also are pertrubed slightly.
How can one show this?